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I needed for my probationary essay; otherwise I should have
had to spend many hours hi the library in laborious research,
He also read over my dissertation with me and was very
friendly - which I could hardly have expected, considering the
great distance in rank between us. I hope he will remember me
later on.' During this visit of Dirichlet's there were excursions
with Weber and others, and Biemann reported to his father
that these human escapes from mathematics did him more
good scientifically than if he had sat all day over his books.
From 1853 (Riemann was then twenty-seven) onward he
thought intensively about mathematical physics. By the end
of the year he had completed the probationary essay, after
many delays due to his growing passion for physical science.
There was still a trial lecture ahead of him before he could be
appointed to the coveted - but unpaid - lectureship. For this
ordeal he had submitted three titles for the faculty to choose
from, hoping and expecting that one of the first two, on which
he had prepared himself, would be selected. But he had incau-
tiously included as his third offering a topic on which Gauss had
pondered for sixty years or more - the foundations of geometry
- and this he had not prepared. Gauss no doubt was curious to
see what a Riemann's 'gloriously fertile originality' would make
of such a profound subject. To Riemann's consternation Gauss
designated the third topic as the one on which Riemann should
prove his mettle as a lecturer before the critical faculty. "So I
am again hi a quandary,' the rash young man confided to his
father, 'since I have to work out this one. I have resumed my
investigation of the connexion between electricity, magnetism,
light, and gravitation, and I have progressed so far that I can
publish it without a qualm. I have become more and more
convinced that Gauss has worked on this subject for years, and
has talked to some friends (Weber among others) about it. I
tell you this in confidence, lest I be thought arrogant - I hope
it is not yet too late for me and that I shall gain recognition as
an independent investigator.*
The strain of carrying on two extremely difficult investiga-
tions simultaneously, while acting as Weber's assistant in the
seminar in mathematical physics, combined with the usual